According to the Mirror's David Maddock, despite the Toffees' new investment from major shareholder Farhad Moshiri, "sources within the club suggest there is a sense of realism that he may force a move in the summer."
The 22-year-old has been in outstanding form this season, as Squawka Football reveals:
The most recent of those goals came in the FA Cup fifth round against Bournemouth, where Lukaku showed predatory reactions in the penalty area to turn home a loose ball, per BT Sport Football:
In November, the Belgian joined an elite cabal of players to have reached 50 Premier League goals before turning 23, per Opta Joe:
United have few recognised options in his position beyond Wayne Rooney and Anthony Martial. Even in light of Marcus Rashford's emergence, the club will almost certainly be pursuing more firepower this summer.
Lukaku's strength, aerial power and killer finish make him a strong choice, though it will require a huge investment to prise the prolific goalscorer away from Everton.
The Red Devils will also be targeting reinforcements at left-back, with Paul Hetherington of the Daily Star Sunday exclusively reporting the club have scouted Hull City's Andrew Robertson, though the 21-year-old is also attracting interest from rivals Manchester City, Arsenal and Tottenham Hotspur.
Robertson is a strong attacking full-back with two goals and four assists to his name in all competitions this season. According to Squawka, the Scot has completed 35 take-ons and created 33 chances in the Championship this year.
Journalist Steven Sutcliffe highlighted Robertson as one of the Tigers' top players defensively:
Indeed, football writer Simon Peach believes the youngster could be poached by a bigger club in the summer:
United could use cover for Luke Shaw, and Robertson represents an excellent candidate to provide that.
The goalkeeper may welcome a return to his home country, though the Red Devils may prefer to keep him for the time being in case they lose David De Gea and are unable to recruit a suitable replacement.